# Pentagons Inside Pentagon

Geometry Level 4

Inside a regular pentagon $$ABCDE$$, construct 5 more regular pentagons of side length $$\dfrac{1}{2}AB$$. The part of the overlapping of these pentagons yields another regular pentagon of side length $$MN$$.

Let $$r=\dfrac{AB}{MN}$$. Find $$\displaystyle \left \lfloor 1000r \right \rfloor$$.

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